The question I always ask myself is this: what would I do if I applied to every graduate school for math in the country but only got admitted to the school with the absolute worst ranking? Would I still decide to accept the admittance and pursue math? I think asking yourself questions such as...
I'm not an expert by any means since I'm just a senior undergrad taking grad courses and doing research, nor do I have much experience outside of PDE. But it certainly seems that PDE fits the mold for the type of problems that you describe. There are seemingly endless projects to work on, that...
No offense, but I think this is probably the worst advice you could possibly give to someone who wants to learn proofs and hopefully move on to high-level mathematics. Cheating? That's beyond ridiculous!
It's about doing whatever it takes to understand the material, beyond that is...
This is false. A buddy of mine just got into Berkeley with a quite low GRE score and a GPA in the 3.5-3.75 range. His letters of recommendation and statement of purpose were key.
I also know another student who got admitted to Princeton. Surely he had a better profile than my friend who...
Summer:
research in partial differential equations
Fall:
Geometry of curves and surfaces (intro diff geom)
linear algebra (graduate)
film analysis
Spanish for high beginners (maybe French instead)
History and culture of native north americans
Homework Statement
Let F be the set of all analytic functions f that map the open unit disc D(0,1) into the set U = \left\{w=u+iv : -2 < u < 2 \right\} such that f(0)=0. Determine whether or not F is a normal family.
Homework Equations
DEF'N: A normal family on a domain (i.e. open and...
Honestly, I think those are the type of thingsyou just need to figure out what works best for you. I don't see any general trends in my classes, some use pens, some use pencils, some use notepads, some use notebooks...I use blank paper and binders. The only thing I would recommend is either...
This is the pure truth right here. Just because some person is an expert on a topic (any topic) doesn't make he or she an expert on what it takes to become an expert (i think that makes sense). True, he has an IDEA of ONE way to become an expert (his way), but there are many paths to any single...
Textbooks are collections of the most important theorems since the birth of modern mathematics. It's taken ALL OF HUMANITY HUNDREDS OF YEARS to compile these results, yet you expect to be able to prove them all on your own in the amount of time you spend on your studies (i.e. much less than a...
Ah yes that makes sense, thanks. Apparently i need to be more careful.
There's still something I'm a bit unclear about though. If one says that a function is never zero, does that imply there exists an ε > 0 such that |f| > ε everywhere?
I can't seem to wrap my head around this concept, I'm hoping you can help me out. Suppose you have a continuous function defined on some compact subset of the plane, say {0 <= x <= 1, 0 <= y <= 1}. I guess the function could be either real or complex valued, but let's just say it's real so we...
What do you think are the chances the drugs were in fact his? I honestly think they're basically slim-to-none, though it seems he's certainly guilty of lacking common sense no matter how the outcome plays out. Other articles report he claims to have traveled to South America to meet a model he...
It does read like a soap opera, and that seems to be the professor's fault since he decided to make comments about his university and the provost to a news reporter. There are plenty other articles online that are less dramatic, notwithstanding how bizarre this entire story is...
Wow old thread, but I understand your dilemma since I'm also still somewhat unsure of my path. I think the issue is that you and I have assumed theoretical physics and mathematical physics are the exact same thing. It's not easy to see the difference, especially because both areas are pretty...
I don't know about Michigan, but I'm pretty sure this is a bad assumption. I'm in the North Carolina system and you can't just switch campuses if you decide you want to go to UNC-Chapel Hill rather than UNC-Greensboro. Also, think of California. I doubt you can just switch into Berkeley or...
I just want to reiterate micro's point about Rudin because I mostly agree with his view. I I won't say I don't like Rudin at all...Rudin is great book, but you have to realize that it is written in the most concise language possible. It does not EXPLAIN anything. Rudin's value lies in its...
Hi, bringing up this old thread because I was stuck on the same problem for a little bit, though for a different reason. I understand the derivation as it is, but the thing that held me back was accounting for the torque due to gravity. Is the torque on each infinitesimal rod element canceled...
I was under the impression that most schools offer it to their students for free. The school buys an annual license and distributes it to the students and faculty. That's the way it works at my school, which is a very large well-known state school. I would check with the software distribution...
i agree your chances at a decent school are probably very slim as it stands now. however if you truly want to pursue math, you can increase those chances over the next year or two by taking classes and finding a professor to research with.
Thanks for all the responses. I think the choice I'm presented with this semester is, if you will, some sort of vague sign that will indicate the direction of my career path, in that choosing algebra will pave the way towards becoming a mathematician, while choosing mechanics will nudge me...
Hey all,
I'm currently a pure math major, though I'm leaning towards going to grad school for applied math, specifically dynamical systems and climate modeling. This semester, upper division abstract algebra and upper division classical mechanics are only offered in the same time-slot. I know...
I'm an undergrad doing research in PDE and my adviser gave me some material to read over the holiday. But I'm getting stuck at the beginning where the divergence theorem is applied to a calculation. Maybe somebody can help me?
Without getting too detailed about the context of the problem...
Thanks for elaborating Deveno
Yep, tell me about it ;) I just finished taking graduate analysis and it was by far the most challenging academic experience of my career.
I'm no expert in neither life, neuroscience, nor psychology...nor mathematics for that matter. That said, I agree wholeheartedly with what you've just written. Furthermore, even if your opinions are wrong, they represent a very healthy self-image: simultaneously confident in your intelligence...
Don't worry, these seemingly trivial type problems were also confusing to me not long ago. I imagine many students have similar troubles. The more you are exposed to proof based math the more you will begin to understand what he's asking for.
To answer your question, you could approach this...
I'm only going to match your level of nit-picky-ness here: How can you assume to know that myself saying I believe something is "obviously not true"? I'm pretty sure it's obviously true that I believe it !
The point being that anyone can pick apart nearly any statement and make it appear...
Look, I completely understand your point. But I think you misunderstand people's motives towards academic careers. A pretty general trait of young ambitious students across the board (beyond the obsession with physics/math) is to reach for their dreams, whether it be medical school, law...
This is kind of off topic, but I don't think lack of a publication over a period of time restricted to a couple handfuls of weeks indicates who was a better participant. I guess yes, technically you were more successful, but success in research requires many things to fall in place...especially...
I don't think gaining a professorship hinges on your GPA and where you went to grad school as much as it seems to. Yes, there are more professors coming from the top schools, but how do you know the reason they're good is because they came from a top school? They could've have gone anywhere...
Unfortunately, for top-tier schools I think it hurts a lot. I once read a thread concerning admissions at one of the tippy-top schools which discussed that while Berkeley is one of the best, it's still accessible to many students who would have absolutely no chance at other places like Harvard...
So wait, you just want to get better at calculations in your head? Because in my opinion, math intuition concerns more conceptual type things. I was going to recommend some competition style problem solving books for better intuition, but that doesn't sound like what you're actually looking for.
Ummm, I'm no grammer nazi but your writing looks relatively fine, and this is just a casual message board.
As far as professional letters, the best advice I can give is be as concise as possible. Keep the sentences short. Don't use things like "so" or "be" (like i just did). For instance, when...
And to answer you question about switching over to physics later on, I'd say the only way this would be possible is if you still take a lot of the lab courses at this level.
In my opinion, the short answer is yes with an asterisk. Mathematical physics, and in particular the study of PDE's, is directly related to physical problems. One of mathematics professors in the analysis group at my university has a NSF grant to study energy decay of the wave equation on...
Yeah, but that doesn't really reflect as much on the department as it does on that subject in general! That class is plug and chug EVERYWHERE. It's really just the nature of a first course in Diff Eq. The theory behind much of it is just a little too advanced for the flocks of aspiring...
Yeah, you're absolutely correct. In fact, I now realize I've learned this before, but apparently the idea is so weird to me that I've put the blinders on this time around.
So for a mostly constant function that takes on a different value on a countable set, the set of discontinuities is not necessarily the same as the set where the function takes on it's different value? If this is true it's probably the most counter-intuitive concept I've come across!
So that holds even when f is identically zero everywhere except for the rationals? Because it seems in that situation, the discontinuities only occur at rational values, which is a countable set.
I definitely see what you're saying if f is identically zero everywhere except for the...
I also thought there was some confusion of the type which you describe arising from the use of multiple textbooks. However, if I pretend for a minute that the only text in existence is "Elementary Classical Analysis" by Marsden and Hoffman, and I flip to chapter 8 (Integration), I find that...
you may be in over your head now, but starting out with this level of rigor will be incredibly amazing for you in the future, assuming you continue in mathematics.